Details

analyze105.0ms (1.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

valid

Compiler

Compiled 57 to 45 computations (21.1% saved)

simplify94.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4987	40
1	4987	40

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.6b

Counts

2 → 1

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.3b	(*.f64 PI.f64 t)
0.4b	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))

rewrite54.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_1541` `add-cbrt-cube_binary64_1549`
20×	`pow1_binary64_1519`
16×	`prod-exp_binary64_1524` `associate-*r/_binary64_1638` `cbrt-unprod_binary64_1546`
14×	`add-sqr-sqrt_binary64_1562`
12×	`associate-l_binary64_1637` `sqrt-div_binary64_1557`
11×	`add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
10×	`pow-prod-down_binary64_1500`
8×	`associate-/r/_binary64_1642` `frac-times_binary64_1569`
7×	`flip--_binary64_1603` `flip3--_binary64_1576`
6×	`flip3-+_binary64_1575` `flip-+_binary64_1602`
5×	`associate-r_binary64_1636`
4×	`sub-neg_binary64_1581` `div-exp_binary64_1526` `cbrt-undiv_binary64_1547` `distribute-lft-in_binary64_1619` `add-log-exp_binary64_1542` `distribute-rgt-in_binary64_1620` `associate-*l/_binary64_1639`
3×	`-commutative_binary64_1645` `times-frac_binary64_1572` `sqrt-prod_binary64_1556` `associate-/l_binary64_1641`
2×	`unswap-sqr_binary64_1605` `associate-/l/_binary64_1643`
1×	`div-sub_binary64_1571` `clear-num_binary64_1580` `associate-/r*_binary64_1640` `frac-2neg_binary64_1570` `div-inv_binary64_1578`

Counts

4 → 109

Calls

4 calls:

22.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
16.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
7.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series584.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

287.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v)))))
232.0ms	(.f64 (sqrt.f64 (+.f64 2 (.f64 v (.f64 -6 v)))) (.f64 (.f64 PI.f64 t) (-.f64 1 (.f64 v v))))
37.0ms	(.f64 5 (.f64 v v))
27.0ms	(*.f64 PI.f64 t)

simplify137.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4963	3590
1	4963	3590

prune228.0ms (4.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	116	5	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	5	122

Merged error: 0.2b

Counts

122 → 5

Compiler

Compiled 4378 to 2728 computations (37.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (.f64 v v))
0.3b	(*.f64 PI.f64 t)
0.6b	(/.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
1.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite53.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64_1572`
51×	`add-sqr-sqrt_binary64_1562`
48×	`add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
34×	`add-exp-log_binary64_1541` `add-cbrt-cube_binary64_1549`
30×	`sqrt-prod_binary64_1556`
27×	`associate-/l*_binary64_1641`
11×	`pow1_binary64_1519`
10×	`prod-exp_binary64_1524` `div-exp_binary64_1526` `cbrt-undiv_binary64_1547` `cbrt-unprod_binary64_1546`
8×	`associate-/r/_binary64_1642`
7×	`associate-/r*_binary64_1640`
6×	`associate-l_binary64_1637` `sqrt-div_binary64_1557`
4×	`pow-prod-down_binary64_1500` `associate-r_binary64_1636` `add-log-exp_binary64_1542` `div-inv_binary64_1578`
3×	`div-sub_binary64_1571` `flip3-+_binary64_1575` `flip-+_binary64_1602` `associate-/l/_binary64_1643`
2×	`-commutative_binary64_1645` `clear-num_binary64_1580` `flip--_binary64_1603` `unswap-sqr_binary64_1605` `frac-2neg_binary64_1570` `flip3--_binary64_1576` `associate-r/_binary64_1638`

Counts

4 → 156

Calls

4 calls:

24.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
10.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
7.0ms	(.f64 5 (.f64 v v))
4.0ms	(*.f64 PI.f64 t)

series489.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

292.0ms	(/.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (.f64 (.f64 PI.f64 t) (-.f64 1 (*.f64 v v))))
128.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
36.0ms	(.f64 5 (.f64 v v))
33.0ms	(*.f64 PI.f64 t)

simplify228.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (167.0ms)

Iter	Nodes	Cost
0	4959	6115
1	4959	6115

prune350.0ms (6.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	167	6	173

Merged error: 0.2b

Counts

173 → 6

Compiler

Compiled 6482 to 4153 computations (35.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 t)
0.4b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (-.f64 1 (.f64 v v)) (*.f64 PI.f64 t)))
0.5b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (-.f64 1 (.f64 v v)) (.f64 PI.f64 t))))
1.0b	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))

rewrite61.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-exp-log_binary64_1541`
52×	`add-sqr-sqrt_binary64_1562`
49×	`add-cbrt-cube_binary64_1549`
46×	`times-frac_binary64_1572`
40×	`*-un-lft-identity_binary64_1577`
38×	`add-cube-cbrt_binary64_1548`
32×	`prod-exp_binary64_1524`
27×	`associate-l_binary64_1637`
25×	`div-exp_binary64_1526`
23×	`sqrt-prod_binary64_1556`
18×	`cbrt-unprod_binary64_1546`
14×	`cbrt-undiv_binary64_1547`
12×	`associate-r_binary64_1636`
10×	`pow1_binary64_1519`
8×	`associate-/r/_binary64_1642`
7×	`associate-/r*_binary64_1640`
6×	`unswap-sqr_binary64_1605` `associate-/l*_binary64_1641`
5×	`1-exp_binary64_1537` `rec-exp_binary64_1525` `associate-*l/_binary64_1639`
4×	`add-log-exp_binary64_1542` `sqrt-div_binary64_1557` `div-inv_binary64_1578`
3×	`flip--_binary64_1603` `flip3--_binary64_1576` `pow-flip_binary64_1503`
2×	`*-commutative_binary64_1645` `clear-num_binary64_1580` `pow-prod-down_binary64_1500` `flip3-+_binary64_1575` `flip-+_binary64_1602` `frac-2neg_binary64_1570` `associate-/l/_binary64_1643`
1×	`sqrt-pow1_binary64_1558` `pow1/2_binary64_1509` `div-sub_binary64_1571` `inv-pow_binary64_1495` `frac-times_binary64_1569` `associate-*r/_binary64_1638`

Counts

4 → 167

Calls

4 calls:

27.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (-.f64 1 (.f64 v v)) (.f64 PI.f64 t))))
13.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (-.f64 1 (.f64 v v)) (*.f64 PI.f64 t)))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
4.0ms	(*.f64 PI.f64 t)

series529.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

288.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6))))) (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (-.f64 1 (.f64 v v)) (.f64 PI.f64 t))))
131.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (-.f64 1 (.f64 v v)) (*.f64 PI.f64 t)))
81.0ms	(/.f64 1 (sqrt.f64 (+.f64 2 (.f64 v (.f64 v -6)))))
28.0ms	(*.f64 PI.f64 t)

simplify157.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4932	5770
1	4932	5770

prune349.0ms (6.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	179	6	185

Merged error: 0.2b

Counts

185 → 6

Compiler

Compiled 6611 to 4256 computations (35.6% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 t)
0.4b	(.f64 v (.f64 PI.f64 t))
0.5b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 2))) (+.f64 (.f64 3 (/.f64 (.f64 v (.f64 v (.f64 PI.f64 t))) (sqrt.f64 2))) (.f64 (.f64 v v) (.f64 t (.f64 PI.f64 (sqrt.f64 2)))))))
9.0b	(.f64 (.f64 v v) (.f64 t (.f64 PI.f64 (sqrt.f64 2))))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_1541` `add-cbrt-cube_binary64_1549`
32×	`pow1_binary64_1519`
19×	`prod-exp_binary64_1524` `pow-prod-down_binary64_1500` `cbrt-unprod_binary64_1546`
17×	`add-sqr-sqrt_binary64_1562`
15×	`add-cube-cbrt_binary64_1548` `*-un-lft-identity_binary64_1577`
9×	`times-frac_binary64_1572`
7×	`associate-l_binary64_1637`
5×	`associate-r_binary64_1636`
4×	`add-log-exp_binary64_1542`
3×	`-commutative_binary64_1645` `associate-/r_binary64_1640` `associate-/l*_binary64_1641`
2×	`associate-/r/_binary64_1642` `flip--_binary64_1603` `flip3--_binary64_1576` `associate-/l/_binary64_1643`
1×	`div-sub_binary64_1571` `clear-num_binary64_1580` `div-exp_binary64_1526` `cbrt-undiv_binary64_1547` `unswap-sqr_binary64_1605` `frac-2neg_binary64_1570` `div-inv_binary64_1578`

Counts

4 → 96

Calls

4 calls:

24.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 2))) (+.f64 (.f64 3 (/.f64 (.f64 v (.f64 v (.f64 PI.f64 t))) (sqrt.f64 2))) (.f64 (.f64 v v) (.f64 t (.f64 PI.f64 (sqrt.f64 2)))))))
13.0ms	(.f64 (.f64 v v) (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
6.0ms	(.f64 v (.f64 PI.f64 t))
5.0ms	(*.f64 PI.f64 t)

series684.0ms (12.4%)

Counts

4 → 12

Calls

4 calls:

553.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 t (.f64 PI.f64 (sqrt.f64 2))) (+.f64 (.f64 3 (/.f64 (.f64 v (.f64 v (.f64 PI.f64 t))) (sqrt.f64 2))) (.f64 (.f64 v v) (.f64 t (.f64 PI.f64 (sqrt.f64 2)))))))
73.0ms	(.f64 (.f64 v v) (.f64 t (.f64 PI.f64 (sqrt.f64 2))))
29.0ms	(.f64 v (.f64 PI.f64 t))
29.0ms	(*.f64 PI.f64 t)

simplify128.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4950	3574
1	4950	3574

prune212.0ms (3.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	108	6	114

Merged error: 0.2b

Counts

114 → 6

Compiler

Compiled 5064 to 2833 computations (44.1% saved)

regimes60.0ms (1.1%)

Compiler: Compiled 604 to 472 computations (21.9% saved)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	63	40
1	63	40

end0.0ms (0%)

sample871.0ms (15.7%)

Algorithm

1×

intervals

Results

526.0ms	8000×	body	80	valid
0.0ms	8×	body	80	nan

Compiler

Compiled 253 to 196 computations (22.5% saved)

Details

analyze105.0ms (1.9%)

sample26.0ms (0.5%)

simplify94.0ms (1.7%)

prune4.0ms (0.1%)

localize16.0ms (0.3%)

rewrite54.0ms (1%)

series584.0ms (10.5%)

simplify137.0ms (2.5%)

prune228.0ms (4.1%)

localize15.0ms (0.3%)

rewrite53.0ms (1%)

series489.0ms (8.8%)

simplify228.0ms (4.1%)

prune350.0ms (6.3%)

localize18.0ms (0.3%)

rewrite61.0ms (1.1%)

series529.0ms (9.6%)

simplify157.0ms (2.8%)

prune349.0ms (6.3%)

localize21.0ms (0.4%)

rewrite52.0ms (0.9%)

series684.0ms (12.4%)

simplify128.0ms (2.3%)

prune212.0ms (3.8%)

regimes60.0ms (1.1%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample871.0ms (15.7%)

Profiling